Hello Mate!
1) You can use the K2 replacing for the content component, but you could not make a look same as 100% the demo, because some of ja extensions works well on k2, others are not possible. so that you need to find extensions having some functions in the Joomla Extension and use them on your site
2) <blockquote>1. How to add a K2 menu item to the Teline II menu – and still retain the Teline II styling?</blockquote>
The menu items are linked pages to display content following the menu type selected. so that when you switched to use k2 component, you need to upgrade one by one in the manual way
3) [PHP]how to pull front page items from K2, rather than Joomla?[/PHP]
as the demo, the front page is using 2 modules, they are ja news pro and ja news fp which are possible to work on k2 component
a ) You need set the featured status for all k2 items you would like, and they will be showed in the ja news fp module
b) you access the ja news pro module and try to select the K2 Source and re-select k2 categories
Good luck